We recall the classical picture about the decoherence effects induced on a quantum sub-system by the interaction with a macroscopic environment. We discuss the need of a rigorous treatment, in mathematically reasonable models, of the dynamical process bringing the system in an entangled state with the environment. We consider a simple system consisting of two particles interacting via a two-body potential and we discuss a rigorous derivation of the asymptotic wave function of the system in the limit of small mass ratio. We apply the result to the explicit computation of the decoherence effect induced on the heavy particle, in concrete examples of quantum evolution.
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